Catechol O-Methyltransferase (COMT) belongs to the class of methyltransferases which catalyse the transfer of a methyl group from the electrophilic donor, S-adenosylmethionine, to a variety of nucleophilic acceptors. COMT methylates hydroxyl groups of substrates with catechol structure and plays an important role in the metabolism of catecholamine neutrotransmitters. The goal of our work is 1) to reproduce quantitatively the reaction energetics of the methylation of catechol by COMT using purely computational techniques, 2) to give an explanation of the factors which lead to the reaction rate enhancement in this class of enzymes compared to the same reaction in water, and 3) to validate our methodology of computing reaction barriers in enzymes. Our theoretical approach, which previously proved successful in describing the energetics of the amide hydrolysis in trypsin, consists of a combination of quantum mechanical and classical free energy perturbation calculations. During all stages of this project, the facilities of the Computer Graphics Laboratory are used for data analysis.